Embodiments of the invention relate generally to transmission lines and more particularly to a resonant balun used in transmission lines.
MRI coils may be single channel antennas or multiple channel phased array antennas. Phased array coils or antennas often need particular circuitry for transporting acquired signal for further processing. For example, in an effort to decouple the channels and the coils associated therewith of the phased array coils, impedance matching or bridging circuitry is often used. This circuitry may include a capacitor, inductor, and a low impedance preamplifier in a receiving loop to effectively create a resonance tank. Often, the use of such circuitry is referred to as preamplifier decoupling. Preamplifier decoupling can beneficially reduce current flow in a receive coil. As such, preamplifier decoupling techniques minimize cross-coupling between channels of a phased array coils.
Preamplifiers employed in matching circuitry often need a “clean” and unperturbed radio frequency (RF) ground reference. However, due to the close proximity between a preamplifier and a coil element, it can be difficult to obtain a clean and unperturbed RF ground reference. One matching technique for obtaining a relatively clean and unperturbed RF ground includes splitting a matching capacitor of the circuitry into two capacitors (the matching capacitor and the second capacitor) of a doubled capacitance and connecting a ground plane of a preamplifier to a so called “virtual” ground of the coil (e.g., a middle point between the matching capacitor and the second capacitor). To complete the match, an inductor is placed in series with an input of the preamplifier. A mathematical model, such as the Reykowski model known in the art, may be followed to allow for calculation or determination of the tuning and matching capacitors and inductance needed for preamp decoupling. Unfortunately, a virtual ground, as used in the matching technique discussed above, is generally not perfectly isolated and unperturbed. As such, the matching circuitry may be adversely affected. 
To address such adverse effects arising from the use of a virtual ground in a matching circuit, a transmission line may be used with the preamplifier low input impedance for achieving inductor like characteristics. The transmission line itself often needs a balun to limit the sheath current. The balun represents an interval of a transmission line with high impedance on the common mode. In MR, where wavelength of the electromagnetic waves is longer that linear dimensions of the coil, the balun is built by creating a resonance tank on the outer shield of the transmission line. A typical transmission line, which needs a balun, is the coaxial cable whose topology includes three conducting paths for the RF current: the external surface of the central conductor, the internal surface of the conducting shield, and the external surface of the shield. This type of transmission line is “unbalanced” in contrast to a “balanced” transmission line. While in the Reykowski model, a classical inductor having impedance linearly dependent on frequency is required, the inductor-like behavior of a shortened transmission line is not a linear function of frequency. Instead, it is proportional to the characteristic impedance of the transmission line (for example, 50 Ohms) and tangential of the electrical length of the line. As such, the mathematical models such as the Reykowski model used to determine tuning and matching capacitance as well as determining inductance often yield only approximations. Further, the magnetic and electrical properties of the balun can also adversely affect the matching circuitry.
It would therefore be desirable to have a system and method capable of decoupling coil elements of an MR coil phase array in such a manner that allows for accurate mathematical modeling. 